Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
488 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q16×#10624382 | C2 | direct (N × H) |
| 18. C2×Dic724 | C4 | semidirect |
| 19. C2×#15668439 | C4 | semidirect |
| 20. Q16×D181 | C4 | semidirect |
| 23. C2×Q16×C181 | C4 | semidirect |
| 44. Dic724 | C2×C4 | semidirect |
| 45. #15668439 | C2×C4 | semidirect |
| 50. Q16×C181 | C2×C4 | semidirect |
| 55. C2×#10624382 | Q16 | direct (N × H) |
| 85. #10624382 | C2×Q16 | direct (N × H) |
| 92. C2×C181 | C4×Q16 | semidirect |
| 94. D181 | C4×Q16 | semidirect |
| 97. C181 | C2×C4×Q16 | semidirect |
| 110. C2×Q16 | #10624382 | direct (N × H) |
| 136. Q16 | C2×#10624382 | direct (N × H) |
| 193. C2 | Q16×#10624382 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10624382 | 2 |
| Q16×#10624382 | 2 |
| C2×#19153885 | 2 |
| C2×#19153879 | 2 |
| C2×C8×#10624382 | 2 |
| C2×Q16×D181 | 2 |
| C2×C4×Q16 | 181 |